Analysis and modelling of MHD instabilities in DIII-D plasmas for the ITER mission

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1 Analysis and modelling of MHD instabilities in DIII-D plasmas for the ITER mission by F. Turco 1 with J.M. Hanson 1, A.D. Turnbull 2, G.A. Navratil 1, C. Paz-Soldan 2, F. Carpanese 3, C.C. Petty 2, T.C. Luce 2 1 Columbia U. 2 General Atomics 3 Dipartimento di Energetica, Politecnico di Milano IAEA-TM, Roma, March 6 th 2015

2 Contents - Making progress by integrating modelling and experiment à MHD spectroscopy to measure the approach to a limit à The MARS-K model for plasma response calculations à The PEST3 model to evaluate Δ trends - The ITER Baseline Scenario: moderate β N, zero torque - The path to high β N and steady-state conditions à Modeling the no-wall limit crossing with non-ideal effects - The steady-state scenarios: high β N, high torque - Low torque at high β N - Discussion and conclusions

3 DIII-D studies demonstration plasmas relevant to these scenarios: ITER Baseline Scenario (IBS) (RWM studies) ITER Steady- State ITER I p (MA) 15 / 9 q Q 10 / 5 DIII-D β N DIII-D Torque (Nm)

4 DIII-D studies demonstration plasmas relevant to these scenarios: ITER Baseline Scenario (IBS) (RWM studies) ITER Steady- State ITER I p (MA) 15 / 9 q Q 10 / 5 DIII-D β N DIII-D Torque (Nm)

5 DIII-D studies demonstration plasmas relevant to these scenarios: ITER Baseline Scenario (IBS) (RWM studies) ITER Steady- State ITER I p (MA) 15 / 9 q Q 10 / 5 DIII-D β N DIII-D Torque (Nm)

6 DIII-D studies demonstration plasmas relevant to these scenarios: ITER Baseline Scenario (IBS) (RWM studies) ITER Steady- State ITER I p (MA) 15 / 9 q Q 10 / 5 DIII-D β N DIII-D Torque (Nm)

7 DIII-D studies demonstration plasmas relevant to these scenarios: ITER Baseline Scenario (IBS) (RWM studies) ITER Steady- State ITER I p (MA) 15 / 9 q Q 10 / 5 DIII-D β N DIII-D Torque (Nm) à Experiment à Modelling

8 Measure the approach to instability: MHD spectroscopy EXP MHD spectroscopy*: A rotating kink-resonant n=1 field is applied with a set of internal coils (I-coils), at f=10 Hz or f=20 Hz ß rotation frequency of the RWM à The plasma response amplitude increases close to a stability boundary à The phase shows a jump Used to probe the proximity to a stability limit Expand the analysis and modeling space to the stable side of the modes * Fasoli PRL1995 * Reimerdes PRL 2004

9 RWMs: slowly growing, slowly rotating kinks MOD The ideal kink instability, with a realistic (non-ideal) wall model, is described by the RWM branch of the dispersion relation à slow growth rate of the order of τ wall (~2.5 ms in DIII-D) The RWM is influenced by à pressure and current profile gradients (ideal MHD) à resonances between the plasma rotation and the thermal particles drift frequencies à non-resonant contributions from fast-particles (NBI ions in DIII-D) In DIII-D, RWMs Cause rotation and β N collapses in the high-q min, high-β N SS plasmas

10 Drift kinetic effects are needed to describe the experimental observations MOD RWMs do not usually appear in fast-rotating, low q min plasmas à kinetic damping of the RWM [Hu et al, PRL2004] γτ W = δw NW δw WW Ideal MHD RWM dispersion relation γτ W = δw NW +δw K δw WW +δw K Kinetic damping physics δw k ~ l ( ω ω E ) f ε n f ψ ez ω ω p ω b + iν eff ω E Precession frequency Bounce frequency Collision frequency Kinetic dependences may extrapolate unfavourably for low external torque and lower fraction of fast beam-generated ions (ITER) à need to validate models for rotation and thermal/fast particles

11 MARS-K model is being validated to predict the stability in unexplored regimes MOD Eigenvalue code, modified to solve for the response to an inhomogeneous forcing function ß External field from the I-coils The model includes - resistive DIII-D wall geometry - rotation, T e, T i, n e from experiment - fast-nbi ions with a Maxwellian slowing down distribution function - radially constant collisionality (for ions and electrons) *Y. Liu et al, Phys. Plasmas 15, (2008)

12 [IBS] MHD stability below the no-wall limit, at zero torque ITER Baseline Scenario (IBS) (RWM studies) ITER Steady- State ITER I p (MA) 15 / 9 q Q 10 / 5 DIII-D β N DIII-D Torque (Nm)

13 [IBS] Stable solution found at moderate to high torque EXP DIII-D IBS demonstration discharges match - plasma shape (LSN) - q 95 = Q = 10 ß β N =1.8, H 98 =1 at q 95 =3 DIII-D can match the predicted torque à Nm Solution non reproducible (50% of cases are unstable)

14 [IBS] At zero torque life is hard... EXP - Narrow operating point found at 1 Nm - Operation at 0 Nm remains elusive Operating on a marginal point à sensitive to small perturbations Ideal no-wall limit β NW ~ Ideal with-wall limit β WW ~ IBS constant β N ~ Non-ideal effects à current profile, rotation, collisionality, resistivity?

15 [IBS] MHD spectroscopy shows that the plasmas are approaching a stability limit EXP Response amplitude increase Non-ideal effects ß à Lower limits Phase jump at ~12-15 krad/s à Typical of no-wall limit crossing Response AMP (G/kA) Response PHI ( ) β N ~ β N ~ Phase jump NBI torque (Nm) NBI torque (Nm) Rotation at ρ~0.7 (krad/s)

16 [IBS] The plasma response trends indicate that non-ideal effects are present EXP - At moderate rotation, the trends are consistent with the ideal model Plasma response amplitude (G/kA) β N /β lim Rotation at ρ=0.7 (krad/s)

17 [IBS] The plasma response trends indicate that non-ideal effects are present EXP - At moderate rotation, the trends are consistent with the ideal model - At higher rotation the response is off trend à kinetic damping? Plasma response amplitude (G/kA) β N /β lim Rotation at ρ=0.7 (krad/s)

18 [IBS] The plasma response trends indicate that non-ideal effects are present EXP - At moderate rotation, the trends are consistent with the ideal model - At higher rotation the response is off trend à kinetic damping? - At very low rotation, with ECH, higher response à collisionality? resistivity? Ideal MHD likely not sufficient to explain the trends Plasma response amplitude (G/kA) β N /β lim Rotation at ρ=0.7 (krad/s)

19 [IBS] MARS-K reproduces only the higher rotation cases EXP - Collisionality is important to reproduce the higher rotation range correctly - MARS does not capture the large increase at very low rotation - The phase is overestimated by ~15-20 Response amplitude(g/ka) MARS-K w/o coll. MARS-K w/ coll. NBI torque (Nm) Response phase ( ) NBI torque (Nm) (B r ) Rotation at ρ~0.7 (krad/s)

20 The path to high β N is a good platform to validate models ITER Baseline Scenario (IBS) (RWM studies) ITER Steady- State ITER I p (MA) 15 / 9 q Q 10 / 5 DIII-D β N DIII-D Torque (Nm) Higher β N Higher q 95

21 Pressure (β N ) scan to cross the no-wall β N limit EXP Increase the pressure with co-ip NBI power à fixed q95, li à Measure the plasma response

22 β N scan: It s crucial to assess the validity of the modeling results MOD Rotation has an impact on the response amplitude The rotation is not constant across the β N values à Sensitivity study: assess impact of rotation on the results

23 β N scan: MHD-only model does not reproduce approach to the no-wall β N limit MOD Previous modelling* showed the MHD model without rotation has a pole at the no-wall limit *Lanctot, PoP2010 Plasma Response Amplitude (GkA) Plasma Response Phase ( ) Experiment MHD only Kinetic Ideal model Model No-wall limit (without rotation) No-wall limit (without rotation) β N

24 β N scan: Drift kinetic model reproduces approach to the no-wall β N limit correctly MOD Previous modelling* showed the MHD model without rotation has a pole at the no-wall limit The pole is eliminated with the full kinetic model (thermal + fast ions) *Lanctot, PoP2010 Plasma Response Amplitude (GkA) Plasma Response Phase ( ) Experiment MHD only Full kinetic Kinetic Model No-wall limit (without rotation) No-wall limit (without rotation) β N

25 β N scan: Drift kinetic model reproduces approach to the no-wall β N limit correctly MOD Previous modelling* showed the MHD model without rotation has a pole at the no-wall limit The pole is eliminated with the full kinetic model (thermal + fast ions) Without fast-ion damping the pole reappears à 45% higher than expt The phase shift is still overestimated above the no-wall limit ITER: very small fast-ion β from NBI à will the plasmas be (45%) more unstable? à Will the fast α-particles be enough to stabilize them? *Lanctot, PoP2010 Plasma Response Amplitude (GkA) Plasma Response Phase ( ) Kinetic Model Experiment MHD only Thermal+fast +45% Thermal No-wall limit (without rotation) ?? No-wall limit (without rotation) β N

26 β N scan: Precession and bounce drift frequencies are the main factors MOD The full model is necessary to reproduce the experiment

27 ITER Baseline Scenario (IBS) (RWM studies) ITER Steady- State ITER I p (MA) 15 / 9 q Q 10 / 5 DIII-D β N DIII-D Torque (Nm) Higher β N Higher Torque

28 [SS] MHD stability is the main challenge for high-β N scenarios EXP - High rotation, β N <=3.6 à can be made passively stable - 2/1 tearing modes arise on β N >3.6 flattop - They degrade the confinement significantly à loss of 20-50% β N β N I p n=1 amplitude (G) , , Time (ms)

29 [SS] Tearing limits are strongly correlated with the ideal with-wall limit MOD The tearing index Δ increases sharply at the ideal wall limit Modelling of the approach to the ideal limit:

30 [SS] Tearing limits are strongly correlated with the ideal with-wall limit MOD The tearing index Δ increases sharply at the ideal wall limit High β N operation Operate with very large, very sensitive Δ? Modelling of the approach to the ideal limit: One solution is to increase the ideal limit: - broaden J and p - change the plasma shape Turnbull, PRL 1995 Turnbull, NF 1998

31 [SS] OFF-axis NBI used to broaden the pressure and current profiles The with-wall β N limits of the OFF-axis cases are ~10% higher

32 [SS] Shape modifications can yield β limit ~6 MOD The with-wall β N limits of the OFF-axis cases are ~10% higher Combined changes of outer gap and squareness: β lim 4.5 à 6 With-wall β N limit Upper squareness

33 [SS] The PEST3 model captures the approach to tearing instability PEST3 Δ Time series of Δ calculated* for experimental equilibria β N ~4 Higher β N >4 cases à Δ shows increasing trend towards the 2/1 mode β N ~ Time (s)

34 [SS] For stable plasmas, Δ decreases The stable cases can have high Δ values But show a stable or decreasing trend on the flattop β N ~

35 [Rotation scan] All the high-β N plasmas have high NBI torque MOD What happens at low rotation, high β N? - Experiment à decrease the rotation at fixed β N, q 95 - Model à capture the rotation effects? fixed equilibrium and n e, T e, n i, P NBI, etc, from a DIII-D plasma a self-similar rotation profile series Plasma rotation and drift frequencies Plasma rotation (krad/s)

36 Rotation effects above the no-wall β N limit EXP Broad peak in the response at krad/s (~1% of the Alfvén velocity) Below the no-wall limit (IBS) the trend is increasing Response AMP (G/kA) MHD spectroscopy Response PHI ( ) Rotation at ρ~0.6 (krad/s)

37 [Rotation scan] MARS-K reproduces the response amplitude with fast-ions MOD MHD spectroscopy With thermal and fast ions, trend and amplitude are well matched...but the phase is underestimated by ~25% If the fast-ions damping is neglected, the results diverge (more) from the measurements Fast-ions destabilizing at high-β N? consistent with β N scan results... Response AMP (G/kA) Response PHI ( ) MARS-K w/ fast ions MARS-K w/o fast ions Rotation at ρ~0.6 (krad/s)

38 Summary and conclusions Modelling the approach to instability: how are we doing? - ITER Baseline Scenario: - Good match at moderate rotation - MARS-K does not reproduce the high response at zero torque - No-wall limit crossing: - MARS-K reproduces very well the response amplitude - The phase is overestimated at high β N - Steady-state scenarios: - PEST3 captures the approach to instability - No rotation dependence! Needed to extrapolate - The rotation dependence at high β N : - MARS-K captures the amplitude trends - The phase trends are not reproduced as well

39 What physics can be added and may be relevant? Collisionality à New MARS-Q: energy dependent collisionality operator Finite ion orbits? The present version of MARS-K assumes a Maxwellian fast-ion distribution (experimental profile in ρ, but no v //, v perp dependence) à Neutral beam ions in DIII-D are strongly anisotropic Large response at zero torque remains a puzzle... Experimental beam-ion distribution (NUBEAM)

40 EXTRAS

41 Current-driven mode: The mode structure is similar to that of the pressure-driven mode The mode eigenfunction is a combination of the main harmonics m=2,3,4,5 The structure of the mode extends radially inward à not only at the edge Comparable to the pressure-driven mode Previously developed RWM feedback techniques and the low q optimizations can be applied to both current-driven and pressure-driven, high β N modes F. Turco/IAEA 2014/St. Petersburg

42 MISK results for rotation scan

43 [IBS] MARS-K reproduces only the higher rotation cases EXP - Collisionality is important to reproduce the higher rotation range correctly - MARS does not capture the large increase at very low rotation - The phase is overestimated by ~15-20 Response amplitude(g/ka) MARS-K w/o coll. MARS-K w/ coll. NBI torque (Nm) Response phase ( ) (B p ) Rotation at ρ~0.7 (krad/s) NBI torque (Nm)

44 [IBS] MARS-K reproduces only the higher rotation cases EXP

45 The Hybrid Regime Addresses the Steady-State Challenges With An Alternative Approach What is a hybrid? à Long duration, high confinement H-mode à More stable to 2/1 tearing modes Final J independent from sources Current density All external current driven in the plasma centre SS High-q min SS Hybrid No alignment issues Most efficient CD q relaxes to hybrid state q min 1 q 3/2 TM q=1 q= , Ideal MHD with-wall limits are β limit 4.5 High q min present limits β lim ~ à predicted β lim ~5

46 The Highest β N Cases Are Limited By MHD At β N 3.6 à 2/1 tearing modes are avoidable At β N 4 à fishbone-like bursts, then 2/1 tearing modes à non-recoverable isolated bursts: β N , τ 1 ms, f khz n=1 Amp (G) τ 50 ms, f~10-15 khz The activity does not decrease with density à not fishbones? May be due to the large fraction of fast particles B dot B dot bursts Time (ms)

47 Hybrid plasmas reach fully NI conditions and β N =3.6 for ~2 τ R EXP Double null plasma shape β N τ R H98y , , P NBI (MW) P ECH (MW) Density (10 19 m -3 ) Stable to the 2/1 TM at β N ~3.6 Loop voltage ~ 0 for ~2 τ R Limited by NBI pulse duration V surf (mv) Time (ms)

48 The Scenario Is Sustained At High Injected Torque Lower Torque Degrades Confinement - 1 neutral beam line added in counter-i p direction (~4 MW) - Same β N, stored energy obtained Confinement decreases by ~20% for 35% lower T P NBI = 11 à 15 MW (35% increase) β N , P NBI (MW) 2/1 TM P ECH (MW) T NBI = 8.8 à 5.6 Nm (35% decrease) NBI torque (Nm) H 98y2 H 98y2 = 1.72 à 1.4 (20% decrease) Time (ms) 2/1 TM

49 With Present Confinement And n e, The DN Hybrid Is Consistent With an FNSF 6.7 MA Scenario INPUTS: R=2.49 m, B t = 6 T q 95 =6.2, ε=3.5 β N =3.66, n lin.av =4 DN 6.7 MA FNSF hybrid Plasma current (MA) scaled Impose I p = 6.7 MA Fix ν* H 98y2 =1.42 SCALED SCENARIO: With n/n G = 0.42 Drive 3.35 MA with ECH+NBI Need P CD = 75 MW P to sustain β N = 172 MW Central Temperature (kev) P INPUT (MW) Density (10 19 m -3 ) (f G = 0.42) Time (s) P CD (MW)

50 With Present Confinement And n e, The SN Hybrid Is Consistent With an ITER 9 MA Scenario INPUTS: R=6.2 m, B t = 5.3 T q 95 =6.2, ε=3.1 β N =3, n lin.av =3.2 SN 9 MA ITER hybrid Plasma current (MA) scaled Impose I p = 9 MA Fix ν* H 98y2 =1.49 Density (10 19 m -3 ) n G (f G = 1.17) SCALED SCENARIO: With n/n G = 1.17 Drive 4.5 MA with ECH+NBI Need P CD = 191 MW P to sustain β N à 175 MW Q = 7.1 Central Temperature (kev) P INPUT (MW) P CD (MW) Time (s)

51 With Present Confinement And lower n e, The SN Hybrid Is Consistent With an ITER 9 MA, Q=4.4 Scenario INPUTS: R=6.2 m, B t = 5.3 T q 95 =6.2, ε=3.1 β N =3, n lin.av =3.2 SN 9 MA ITER hybrid Plasma current (MA) scaled Impose I p = 9 MA Scale f GW H 98y2 =1.49 Density (10 19 m -3 ) n G (f G = 0.9) SCALED SCENARIO: With n/n G = 0.9 Drive 4.5 MA with ECH+NBI Need P CD = 112 MW P to sustain β N à 233 MW Q = 4.4 Central Temperature (kev) P INPUT (MW) P CD (MW) Time (s)

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